Gene expression in Saccharomyces cerevisiae is regulated at multiple levels. Genomic and epigenomic mapping of transcription factors and chromatin factors has led to the delineation of various modular regulatory elements-enhancers (upstream activating sequences), core promoters, 5' untranslated regions (5' UTRs) and transcription terminators/3' untranslated regions (3' UTRs). However, only a few of these elements have been tested in combinations with other elements and the functional interactions between the different modular regulatory elements remain under explored. We describe a simple and rapid approach to build a combinatorial library of regulatory elements and have used this library to study 26 different enhancers, core promoters, 5' UTRs and transcription terminators/3' UTRs to estimate the contribution of individual regulatory parts in gene expression. Our combinatorial analysis shows that while enhancers initiate gene expression, core promoters modulate the levels of enhancer-mediated expression and can positively or negatively affect expression from even the strongest enhancers. Principal component analysis (PCA) indicates that enhancer and promoter function can be explained by a single principal component while UTR function involves multiple functional components. The PCA also highlights outliers and suggest differences in mechanisms of regulation by individual elements. Our data also identify numerous regulatory cassettes composed of different individual regulatory elements that exhibit equivalent gene expression levels. These data thus provide a catalog of elements that could in future be used in the design of synthetic regulatory circuits.